It came as he updated the House of Commons on how the government is dealing with the impact of new strains of the virus on its plans to exit lockdown.
He also confirmed a large number of the identified cases were in Bolton and Blackburn with Darwen.
He said: “There’s now 2,323 confirmed cases of B.1617.2 in the UK – 483 of these cases have been seen in Bolton and Blackburn with Darwen, where it’s now the dominant strain.
“Cases there have doubled in the last week and are rising in all age groups.
“In Blackburn, hospitalisations are stable with eight people currently in hospital with Covid, and in Bolton 19 people are now in hospital with coronavirus – the majority of whom are eligible for a vaccine but haven’t yet had a vaccine.
“This shows the new variant is not tending to penetrate into older, vaccinated groups and it underlines again the importance of getting the jab especially – but not only – amongst the vulnerable age groups.”
The health secretary said people aged 37 will be offered the vaccine from Tuesday and this will be expanded further “later in the week”.
He said: “From tomorrow, I can confirm that we will be inviting people aged 37 to come forward before expanding this further later in the week.”
It has also been confirmed that 36-year-olds will be offered the jab from Wednesday.
He added that there are now fewer than 1,000 people in hospital in the UK with coronavirus and the average number of daily deaths is nine.
“This progress means we are able to take step three in our roadmap today, carefully easing some of the restrictions we have all endured,” he told MPs.
“People have missed the things that makes life worth living, businesses have endured hardship and everybody has made sacrifices.
“We must be humble in the face of this virus - we all learned over the past year that in a pandemic we must look not just at where we are today but where the evidence shows we may be in weeks and months down the track.”
He also confirmed surge testing will take place in Bedford after a rise in Indian variant cases of coronavirus.
He told the Commons: “There are now 86 local authorities where there are five or more confirmed cases.
“The next biggest case of concern is Bedford where we are surging testing – and I would urge everybody in Bedford to exercise caution and engage in testing where it is available.”
Informing MPs of the latest scientific assessment on the Indian variant, the health secretary continued: “The early evidence suggests that B1617.2 is more transmissible than the previously dominant B1117 variant. We do not yet know to what extent it is more transmissible.
“While we also don’t have the complete picture on the impact of the vaccine, the early laboratory data from Oxford University corroborates the evidence from Bolton Hospital and the initial observational data from India that vaccines are effective against this variant.”
It came as Prime Minister Boris Johnson and health experts continued to warn the public to be careful when resuming social contact such as hugging.